Simplify the following expression: $ t = \dfrac{-7z - 5}{z + 9} + \dfrac{9}{8} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-7z - 5}{z + 9} \times \dfrac{8}{8} = \dfrac{-56z - 40}{8z + 72} $ Multiply the second expression by $\dfrac{z + 9}{z + 9}$ $ \dfrac{9}{8} \times \dfrac{z + 9}{z + 9} = \dfrac{9z + 81}{8z + 72} $ Therefore $ t = \dfrac{-56z - 40}{8z + 72} + \dfrac{9z + 81}{8z + 72} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-56z - 40 + 9z + 81}{8z + 72} $ $t = \dfrac{-47z + 41}{8z + 72}$